The tribulation period is compared to the times of Noah and Lot by Jesus in Luke 17:28. Most people argue over whether the time frame Jesus was talking about in that passage was pre-trib or post-trib. In doing so, they miss an important point. The two circumstances that the Noah and Lot situations have in common are the removal of the righteous and the judgment of the unbelievers. From these two accounts, we see that God prefers to remove His own when danger is involved. They also miss the point that the wicked are removed, not the righteous.
Noah didn't go anywhere. He was instructed to build a boat, which saved/protected him and his families. Lot was instructed to leave Sodom, which got him out of harms way/protected him. They weren't removed from the Earth. They remained and endured because of God's protection.
The righteous were removed from the scene where the judgment took place and were not subject to the judgment. For Noah to have been left where the judgment was inflicted, he would have been under water with those who were being judged.
God removed Noah from the judgment of the water by way of an ark, and God will removed the Church from the judgment of the earth by way of the Rapture.